TSTP Solution File: GRP040-4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP040-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:18:53 EDT 2024
% Result : Unsatisfiable 0.09s 0.35s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP040-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n024.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue Apr 30 00:24:51 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.09/0.32 % Drodi V3.6.0
% 0.09/0.35 % Refutation found
% 0.09/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.35 fof(f1,axiom,(
% 0.09/0.35 (![X]: (product(identity,X,X) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f3,axiom,(
% 0.09/0.35 (![X]: (product(inverse(X),X,identity) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f5,axiom,(
% 0.09/0.35 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f6,axiom,(
% 0.09/0.35 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f7,axiom,(
% 0.09/0.35 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f9,axiom,(
% 0.09/0.35 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,inverse(B),C)| subgroup_member(C) ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f10,axiom,(
% 0.09/0.35 subgroup_member(identity) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f11,axiom,(
% 0.09/0.35 (![A]: (( ~ subgroup_member(A)| subgroup_member(inverse(A)) ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f12,axiom,(
% 0.09/0.35 (![A,B,C,D]: (( ~ product(A,B,C)| ~ product(A,D,C)| D = B ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f14,axiom,(
% 0.09/0.35 (![A,B]: (( subgroup_member(element_in_O2(A,B))| subgroup_member(B)| subgroup_member(A) ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f15,axiom,(
% 0.09/0.35 (![A,B]: (( product(A,element_in_O2(A,B),B)| subgroup_member(B)| subgroup_member(A) ) ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f16,hypothesis,(
% 0.09/0.35 ~ subgroup_member(a) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f17,hypothesis,(
% 0.09/0.35 subgroup_member(b) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f18,hypothesis,(
% 0.09/0.35 ~ subgroup_member(d) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f19,hypothesis,(
% 0.09/0.35 product(b,inverse(a),c) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f20,hypothesis,(
% 0.09/0.35 product(a,c,d) ),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f21,negated_conjecture,(
% 0.09/0.35 (![A]: (inverse(inverse(A)) = A ))),
% 0.09/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.35 fof(f22,plain,(
% 0.09/0.35 ![X0]: (product(identity,X0,X0))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f1])).
% 0.09/0.35 fof(f24,plain,(
% 0.09/0.35 ![X0]: (product(inverse(X0),X0,identity))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f3])).
% 0.09/0.35 fof(f26,plain,(
% 0.09/0.35 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f5])).
% 0.09/0.35 fof(f27,plain,(
% 0.09/0.35 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f6])).
% 0.09/0.35 fof(f28,plain,(
% 0.09/0.35 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f27])).
% 0.09/0.35 fof(f29,plain,(
% 0.09/0.35 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f7])).
% 0.09/0.35 fof(f30,plain,(
% 0.09/0.35 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f29])).
% 0.09/0.35 fof(f33,plain,(
% 0.09/0.35 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,inverse(B),C)))|subgroup_member(C))),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f9])).
% 0.09/0.35 fof(f34,plain,(
% 0.09/0.35 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,inverse(X1),X2)|subgroup_member(X2))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f33])).
% 0.09/0.35 fof(f35,plain,(
% 0.09/0.35 subgroup_member(identity)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f10])).
% 0.09/0.35 fof(f36,plain,(
% 0.09/0.35 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f11])).
% 0.09/0.35 fof(f37,plain,(
% 0.09/0.35 ![B,D]: ((![A,C]: (~product(A,B,C)|~product(A,D,C)))|D=B)),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f12])).
% 0.09/0.35 fof(f38,plain,(
% 0.09/0.35 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|X3=X1)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f37])).
% 0.09/0.35 fof(f41,plain,(
% 0.09/0.35 ![A]: ((![B]: (subgroup_member(element_in_O2(A,B))|subgroup_member(B)))|subgroup_member(A))),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f14])).
% 0.09/0.35 fof(f42,plain,(
% 0.09/0.35 ![X0,X1]: (subgroup_member(element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f41])).
% 0.09/0.35 fof(f43,plain,(
% 0.09/0.35 ![A]: ((![B]: (product(A,element_in_O2(A,B),B)|subgroup_member(B)))|subgroup_member(A))),
% 0.09/0.35 inference(miniscoping,[status(esa)],[f15])).
% 0.09/0.35 fof(f44,plain,(
% 0.09/0.35 ![X0,X1]: (product(X0,element_in_O2(X0,X1),X1)|subgroup_member(X1)|subgroup_member(X0))),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f43])).
% 0.09/0.35 fof(f45,plain,(
% 0.09/0.35 ~subgroup_member(a)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f16])).
% 0.09/0.35 fof(f46,plain,(
% 0.09/0.35 subgroup_member(b)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f17])).
% 0.09/0.35 fof(f47,plain,(
% 0.09/0.35 ~subgroup_member(d)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f18])).
% 0.09/0.35 fof(f48,plain,(
% 0.09/0.35 product(b,inverse(a),c)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f19])).
% 0.09/0.35 fof(f49,plain,(
% 0.09/0.35 product(a,c,d)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f20])).
% 0.09/0.35 fof(f50,plain,(
% 0.09/0.35 ![X0]: (inverse(inverse(X0))=X0)),
% 0.09/0.35 inference(cnf_transformation,[status(esa)],[f21])).
% 0.09/0.35 fof(f51,plain,(
% 0.09/0.35 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(inverse(X1))|~product(X0,X1,X2)|subgroup_member(X2))),
% 0.09/0.35 inference(paramodulation,[status(thm)],[f50,f34])).
% 0.09/0.35 fof(f55,plain,(
% 0.09/0.35 subgroup_member(inverse(b))),
% 0.09/0.35 inference(resolution,[status(thm)],[f46,f36])).
% 0.09/0.35 fof(f58,plain,(
% 0.09/0.35 spl0_0 <=> subgroup_member(identity)),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f60,plain,(
% 0.09/0.35 ~subgroup_member(identity)|spl0_0),
% 0.09/0.35 inference(component_clause,[status(thm)],[f58])).
% 0.09/0.35 fof(f66,plain,(
% 0.09/0.35 spl0_2 <=> ~subgroup_member(inverse(X0))|subgroup_member(X0)),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f67,plain,(
% 0.09/0.35 ![X0]: (~subgroup_member(inverse(X0))|subgroup_member(X0)|~spl0_2)),
% 0.09/0.35 inference(component_clause,[status(thm)],[f66])).
% 0.09/0.35 fof(f69,plain,(
% 0.09/0.35 ![X0]: (~subgroup_member(identity)|~subgroup_member(inverse(X0))|subgroup_member(X0))),
% 0.09/0.35 inference(resolution,[status(thm)],[f22,f51])).
% 0.09/0.35 fof(f70,plain,(
% 0.09/0.35 ~spl0_0|spl0_2),
% 0.09/0.35 inference(split_clause,[status(thm)],[f69,f58,f66])).
% 0.09/0.35 fof(f71,plain,(
% 0.09/0.35 $false|spl0_0),
% 0.09/0.35 inference(forward_subsumption_resolution,[status(thm)],[f60,f35])).
% 0.09/0.35 fof(f72,plain,(
% 0.09/0.35 spl0_0),
% 0.09/0.35 inference(contradiction_clause,[status(thm)],[f71])).
% 0.09/0.35 fof(f93,plain,(
% 0.09/0.35 ![X0]: (product(X0,inverse(X0),identity))),
% 0.09/0.35 inference(paramodulation,[status(thm)],[f50,f24])).
% 0.09/0.35 fof(f103,plain,(
% 0.09/0.35 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(inverse(X1))|subgroup_member(multiply(X0,X1)))),
% 0.09/0.35 inference(resolution,[status(thm)],[f26,f51])).
% 0.09/0.35 fof(f109,plain,(
% 0.09/0.35 ![X0]: (~subgroup_member(inverse(X0))|subgroup_member(multiply(inverse(b),X0)))),
% 0.09/0.35 inference(resolution,[status(thm)],[f103,f55])).
% 0.09/0.35 fof(f118,plain,(
% 0.09/0.35 spl0_10 <=> subgroup_member(d)),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f119,plain,(
% 0.09/0.35 subgroup_member(d)|~spl0_10),
% 0.09/0.35 inference(component_clause,[status(thm)],[f118])).
% 0.09/0.35 fof(f126,plain,(
% 0.09/0.35 spl0_12 <=> subgroup_member(c)),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f127,plain,(
% 0.09/0.35 subgroup_member(c)|~spl0_12),
% 0.09/0.35 inference(component_clause,[status(thm)],[f126])).
% 0.09/0.35 fof(f140,plain,(
% 0.09/0.35 ![X0]: (~product(a,c,X0)|d=X0)),
% 0.09/0.35 inference(resolution,[status(thm)],[f28,f49])).
% 0.09/0.35 fof(f161,plain,(
% 0.09/0.35 d=multiply(a,c)),
% 0.09/0.35 inference(resolution,[status(thm)],[f140,f26])).
% 0.09/0.35 fof(f191,plain,(
% 0.09/0.35 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(identity,X1,X3)|product(X0,X2,X3))),
% 0.09/0.35 inference(resolution,[status(thm)],[f30,f93])).
% 0.09/0.35 fof(f232,plain,(
% 0.09/0.35 ![X0,X1,X2]: (~product(identity,X0,X1)|product(X2,multiply(inverse(X2),X0),X1))),
% 0.09/0.35 inference(resolution,[status(thm)],[f191,f26])).
% 0.09/0.35 fof(f351,plain,(
% 0.09/0.35 ![X0,X1]: (product(X0,multiply(inverse(X0),X1),X1))),
% 0.09/0.35 inference(resolution,[status(thm)],[f232,f22])).
% 0.09/0.35 fof(f372,plain,(
% 0.09/0.35 ![X0,X1,X2]: (~product(X0,X1,X2)|X1=multiply(inverse(X0),X2))),
% 0.09/0.35 inference(resolution,[status(thm)],[f351,f38])).
% 0.09/0.35 fof(f384,plain,(
% 0.09/0.35 ![X0,X1]: (product(inverse(X0),multiply(X0,X1),X1))),
% 0.09/0.35 inference(paramodulation,[status(thm)],[f50,f351])).
% 0.09/0.35 fof(f415,plain,(
% 0.09/0.35 product(inverse(a),d,c)),
% 0.09/0.35 inference(paramodulation,[status(thm)],[f161,f384])).
% 0.09/0.35 fof(f471,plain,(
% 0.09/0.35 ![X0]: (~product(inverse(a),X0,c)|X0=d)),
% 0.09/0.35 inference(resolution,[status(thm)],[f415,f38])).
% 0.09/0.35 fof(f476,plain,(
% 0.09/0.35 spl0_17 <=> subgroup_member(inverse(a))),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f477,plain,(
% 0.09/0.35 subgroup_member(inverse(a))|~spl0_17),
% 0.09/0.35 inference(component_clause,[status(thm)],[f476])).
% 0.09/0.35 fof(f478,plain,(
% 0.09/0.35 ~subgroup_member(inverse(a))|spl0_17),
% 0.09/0.35 inference(component_clause,[status(thm)],[f476])).
% 0.09/0.35 fof(f497,plain,(
% 0.09/0.35 inverse(a)=multiply(inverse(b),c)),
% 0.09/0.35 inference(resolution,[status(thm)],[f372,f48])).
% 0.09/0.35 fof(f636,plain,(
% 0.09/0.35 spl0_20 <=> element_in_O2(inverse(a),c)=d),
% 0.09/0.35 introduced(split_symbol_definition)).
% 0.09/0.35 fof(f637,plain,(
% 0.09/0.35 element_in_O2(inverse(a),c)=d|~spl0_20),
% 0.09/0.35 inference(component_clause,[status(thm)],[f636])).
% 0.09/0.35 fof(f639,plain,(
% 0.09/0.35 subgroup_member(c)|subgroup_member(inverse(a))|element_in_O2(inverse(a),c)=d),
% 0.09/0.35 inference(resolution,[status(thm)],[f44,f471])).
% 0.09/0.35 fof(f640,plain,(
% 0.09/0.35 spl0_12|spl0_17|spl0_20),
% 0.09/0.35 inference(split_clause,[status(thm)],[f639,f126,f476,f636])).
% 0.09/0.35 fof(f700,plain,(
% 0.09/0.35 $false|~spl0_10),
% 0.09/0.35 inference(forward_subsumption_resolution,[status(thm)],[f119,f47])).
% 0.09/0.35 fof(f701,plain,(
% 0.09/0.35 ~spl0_10),
% 0.09/0.35 inference(contradiction_clause,[status(thm)],[f700])).
% 0.09/0.35 fof(f729,plain,(
% 0.09/0.35 subgroup_member(inverse(c))|~spl0_12),
% 0.09/0.35 inference(resolution,[status(thm)],[f127,f36])).
% 0.09/0.35 fof(f752,plain,(
% 0.09/0.35 subgroup_member(a)|~spl0_17|~spl0_2),
% 0.09/0.35 inference(resolution,[status(thm)],[f477,f67])).
% 0.09/0.35 fof(f753,plain,(
% 0.09/0.35 $false|~spl0_17|~spl0_2),
% 0.09/0.35 inference(forward_subsumption_resolution,[status(thm)],[f752,f45])).
% 0.09/0.35 fof(f754,plain,(
% 0.09/0.35 ~spl0_17|~spl0_2),
% 0.09/0.35 inference(contradiction_clause,[status(thm)],[f753])).
% 0.09/0.35 fof(f761,plain,(
% 0.09/0.35 subgroup_member(multiply(inverse(b),c))|~spl0_12),
% 0.09/0.35 inference(resolution,[status(thm)],[f729,f109])).
% 0.09/0.35 fof(f762,plain,(
% 0.09/0.35 subgroup_member(inverse(a))|~spl0_12),
% 0.09/0.35 inference(forward_demodulation,[status(thm)],[f497,f761])).
% 0.09/0.35 fof(f772,plain,(
% 0.09/0.35 $false|spl0_17|~spl0_12),
% 0.09/0.35 inference(forward_subsumption_resolution,[status(thm)],[f762,f478])).
% 0.09/0.35 fof(f773,plain,(
% 0.09/0.35 spl0_17|~spl0_12),
% 0.09/0.35 inference(contradiction_clause,[status(thm)],[f772])).
% 0.09/0.35 fof(f779,plain,(
% 0.09/0.35 subgroup_member(d)|subgroup_member(c)|subgroup_member(inverse(a))|~spl0_20),
% 0.09/0.35 inference(paramodulation,[status(thm)],[f637,f42])).
% 0.09/0.35 fof(f780,plain,(
% 0.09/0.35 spl0_10|spl0_12|spl0_17|~spl0_20),
% 0.09/0.35 inference(split_clause,[status(thm)],[f779,f118,f126,f476,f636])).
% 0.09/0.35 fof(f781,plain,(
% 0.09/0.35 $false),
% 0.09/0.35 inference(sat_refutation,[status(thm)],[f70,f72,f640,f701,f754,f773,f780])).
% 0.09/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.37 % Elapsed time: 0.049909 seconds
% 0.09/0.37 % CPU time: 0.275817 seconds
% 0.09/0.37 % Total memory used: 59.765 MB
% 0.09/0.37 % Net memory used: 59.325 MB
%------------------------------------------------------------------------------